Percentage, profit and loss
Class 7 Maths · Comparing quantities · 31 questions with answers
Profit and loss questions are usually lost on one thing: what the percentage is of. Profit percent is always on the cost price, discount is always on the marked price, and a child who takes it of the wrong number gets an answer that looks reasonable and is wrong. These questions build up to the ones that work backwards, which is where that confusion shows.
- Converts fluently between fractions, decimals and percentages
- Finds a percentage of a quantity without a formula
- Calculates profit or loss percent on the cost price
- Works backwards from selling price to cost price
- States what each percentage is a percentage of
Exercise 1 of 3 · 11 questions
Convert or calculate.
Write the answer · Warm-up
Here’s one done for you
12% of 500 = 60. Percent means 'out of a hundred', so 12% is 12/100, and 12/100 of 500 is 60. A child who reads every percentage as a fraction out of a hundred rarely needs a formula for anything in this chapter - the formula is what people fall back on when the meaning was never clear.
- 1)25% as a fraction in lowest terms
- 2)3/5 as a percentage
- 3)0.35 as a percentage
- 4)12% of 500
- 5)40% of 250
- 6)15% of 80
- 7)7/20 as a percentage
- 8)0.125 as a percentage
- 9)18% of 350
- 10)22% of 150
- 11)35% of 240
Answers
- 1) 1/4. 25/100 simplifies by 25.
- 2) 60%. 3/5 = 60/100.
- 3) 35%. Multiply by 100.
- 4) 60. 12/100 × 500 = 60.
- 5) 100. 40/100 × 250 = 100.
- 6) 12. 15/100 × 80 = 12.
- 7) 35%. 7/20 = 35/100.
- 8) 12.5%. Multiply by 100.
- 9) 63. 18/100 × 350 = 63.
- 10) 33. 22/100 × 150 = 33.
- 11) 84. 35/100 × 240 = 84.
Exercise 2 of 3 · 10 questions
Find the profit or loss, and the profit or loss percent.
Write the answer · Guided
Here’s one done for you
CP ₹400, SP ₹460. The profit is 460 - 400 = ₹60. Profit percent is the profit as a fraction of the cost price: 60/400 × 100 = 15%. Always the cost price, never the selling price - dividing by 460 here would give about 13%, which looks perfectly plausible and is wrong. If your child can say what the percentage is of before dividing, this chapter is largely done.
- 1)Cost price ₹400, selling price ₹460
- 2)Cost price ₹250, selling price ₹200
- 3)Cost price ₹1,200, selling price ₹1,500
- 4)Cost price ₹800, selling price ₹720
- 5)Cost price ₹60, selling price ₹75
- 6)Cost price ₹500, selling price ₹575
- 7)Cost price ₹900, selling price ₹720
- 8)Cost price ₹150, selling price ₹180
- 9)Cost price ₹2,000, selling price ₹2,500
- 10)Cost price ₹640, selling price ₹560
Answers
- 1) Profit ₹60. Profit percent = 60/400 × 100 = 15%.
- 2) Loss ₹50. Loss percent = 50/250 × 100 = 20%.
- 3) Profit ₹300. Profit percent = 300/1200 × 100 = 25%.
- 4) Loss ₹80. Loss percent = 80/800 × 100 = 10%.
- 5) Profit ₹15. Profit percent = 15/60 × 100 = 25%.
- 6) Profit ₹75. Profit percent = 75/500 × 100 = 15%.
- 7) Loss ₹180. Loss percent = 180/900 × 100 = 20%.
- 8) Profit ₹30. Profit percent = 30/150 × 100 = 20%.
- 9) Profit ₹500. Profit percent = 500/2000 × 100 = 25%.
- 10) Loss ₹80. Loss percent = 80/640 × 100 = 12.5%.
Exercise 3 of 3 · 10 questions
Work these out. Show the working.
Write the answer · Practice
Here’s one done for you
The shirt: a 20% discount means the customer pays 80% of the marked price, so 80% of the marked price is ₹800 and the marked price is 800 × 100 ÷ 80 = ₹1,000. The mistake this question catches is adding 20% of 800 back on, which gives ₹960 - wrong, because the 20% was of the marked price, not of what was paid. Working-backwards questions are the ones worth slowing down on.
- 1)A shopkeeper buys a cycle for ₹2,400 and sells it at a profit of 15%. What is the selling price?
- 2)A book bought for ₹250 is sold for ₹225. What is the loss percent?
- 3)20% of a class of 45 students were absent. How many were present?
- 4)A shirt costs ₹800 after a 20% discount on its marked price. What was the marked price?
- 5)A trader sells a watch for ₹1,140 at a loss of 5%. What was the cost price?
- 6)A bag is sold for ₹900 at a profit of 25%. What was the cost price?
- 7)After a 15% discount a jacket costs ₹1,275. What was the marked price?
- 8)A phone bought for ₹9,000 is sold at a loss of 8%. What is the selling price?
- 9)35% of a school's 640 students walk to school. How many do not?
- 10)A price rises from ₹250 to ₹300. By what percentage did it rise?
Answers
- 1) Profit = 15% of 2400 = ₹360, so the selling price is 2400 + 360 = ₹2,760.
- 2) Loss = 250 - 225 = ₹25. Loss percent = 25/250 × 100 = 10%.
- 3) Absent = 20% of 45 = 9, so 45 - 9 = 36 students were present.
- 4) After a 20% discount the price is 80% of the marked price, so 80% of MP = 800, giving MP = 800 × 100 ÷ 80 = ₹1,000.
- 5) A 5% loss means the selling price is 95% of the cost price, so 95% of CP = 1140, giving CP = 1140 × 100 ÷ 95 = ₹1,200.
- 6) A 25% profit means the selling price is 125% of the cost price, so CP = 900 × 100 ÷ 125 = ₹720.
- 7) After a 15% discount the price is 85% of the marked price, so MP = 1275 × 100 ÷ 85 = ₹1,500.
- 8) Loss = 8% of 9000 = ₹720, so the selling price is 9000 - 720 = ₹8,280.
- 9) 35% of 640 = 224 walk, so 640 - 224 = 416 do not.
- 10) Rise = ₹50. Percentage rise = 50/250 × 100 = 20%.
While your child works
- One question fixes most errors here: 'a percentage of what?' Profit percent is of the cost price. Discount is of the marked price.
- Working backwards is where marks are actually lost. If the sheet runs long, skip a conversion question rather than one of the last two.
- Check the answer is sensible. A profit that makes the selling price lower than the cost price means something has been divided the wrong way round.